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## MATH 2 UCLA Probability Questions

### Question Description

2. A hospital receives 90% of its Covid-19 vaccine from Company Red and

the remainder from Company Blue.

• From Company Red, 15% of the vials are ineffective.
• From Company Blue, 25% are ineffective.
• A hospital tests n = 15 randomly selected vials from one shipment for

their effectiveness.

(a) (5 points) Compute the probability that exactly 3 of these 15 vials

are ineffective if this shipment comes from Company Red. (No need

to simplify.)

(b) (5 points) Compute the probability that exactly 3 of these 15 vials

are ineffective if this shipment comes from Company Blue. (No need

to simplify.)

(c) (5 points) Compute the probability that exactly 3 of these 15 vials

are ineffective. (No need to simplify.)

(d) (5 points) Compute the conditional probability that this shipment

come from Company Red, given that exactly three of these 15 vials

are ineffective. (No need to simplify.)

3. Friendly Instructor Cereal began placing one of the 250 Pokemon figurines

randomly into each cereal box they sold.

(a) (5 points) On the average, how many boxes of cereal should you buy

until you have three copies of the Pikachu figurine?

(b) (10 points) Approximate the probability that there are no Pikachu

figurines at all in 500 boxes.

.(c) (10 points) On the average, how many boxes of cereal should you buy

until you obtain a complete collection consisting of all the pokemons?

Give an approximate answer. (Hint: use Taylors expansion)

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